MOSCOW—A Russian court unexpectedly moved up the date for announcing a verdict in a closely watched fraud case against a prominent opposition activist to Tuesday, a spokesman said Monday.

Supporters of the activist, Alexei Navalny, had called for a public meeting on Jan. 15, the date originally scheduled for the verdict’s announcement in the case. Those appeals had drawn tens of thousands of pledges to attend on social networks, even as Russian Internet regulators ordered several of the pages dedicated to the event blocked...